Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H2

Authors

Yingbin Ge, Central Washington University
Robert C. Rittenhouse, Central Washington University
Jacob C. Buchanan, Central Washington University
Benjamin Livingston, Oregon State University

Document Type

Article

Department or Administrative Unit

Chemistry

Publication Date

5-1-2014

Abstract

We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the S₀ ground electronic state and the S₁ and T₁ excited states of H₂. The spreadsheet calculations circumvent the construction and diagonalization of the Fock matrix and thus can be accomplished by any undergraduate chemistry student with basic calculus skills. The wave functions of the S₀, S₁, and T₁ states of H₂ are constructed from the symmetry-adapted bonding and antibonding molecular orbitals (MO). All quantum mechanical integrals are estimated using the Monte Carlo integration method. Due to the stochastic nature of the spreadsheet calculations, 25 runs were carried out to obtain the mean energy of the S₀, S₁, and T₁ electronic states of H₂. The accuracy of the spreadsheet calculations is comparable to that of the HF/STO-3G calculations. The atomic and molecular orbitals and the energy components can be easily calculated and plotted for better visualization and understanding of essential quantum chemical concepts. This spreadsheet can also be adapted to tackle a wider range of quantum chemistry problems with different levels of complexity.

Comments

This article was originally published in Journal of Chemical Education with an ACS AuthorChoice License. The full-text article from the publisher can be found here.

Recommended Citation

Ge, Y., Rittenhouse, R. C., Buchanan, J. C., & Livingston, B. (2014). Using a Spreadsheet To Solve the Schrödinger Equations for the Energies of the Ground Electronic State and the Two Lowest Excited States of H2. Journal of Chemical Education, 91(6), 853–859. https://doi.org/10.1021/ed400693p

Journal

Journal of Chemical Education

Rights

Copyright © 2014 The American Chemical Society and Division of Chemical Education, Inc.